Those whose destiny is the lake of fire, the second death are already dead. They were dead in their life in their body of flesh, and they are still just as dead after they are dead. Never were they alive spiritually. To be spiritually dead is to not be alive in the spirit. The only way we become spiritually alive is to be born of God, otherwise all are dead. God's judgment is fair and righteous and all these dead ones deserve the second death. They being dead died in life as dead men, and they at the judgment still being dead can not reign with God and Christ, never having been born again. Jesus tells us about them this, 'let the dead bury the dead, but as for you, come and follow me'. So does Christ relate to all those He has foreknown beforehand in love. Ephesians 2.
To have life according to your own works, is specifically taught against. Here in Rev 20, the judgment is either the second death or the Book of Life, according to their works. The Book of Life has the names of all those born of God, given to Christ by the Father, John 17. Christ had already descended into hell and delivered the righteous saved dead, OT saints and led them captive, taking them into heaven. So the only ones left in Hell are these new dead who died in their sins after the resurrection and the ones who died. To die in your sins means your sins are not forgiven for the sake of His name, and that means eternal torment. That rich man in hell is still in hell today 2000 years later.
The lake of fire second death has a sense of finality, a final judgment, hell being a temporary abode of the dead. Hell ends in this creation with the creation of new heavens and new earth, so this is where all dead go, while all who are alive reign with God and Christ in a new universe.
Rev 20
The Great White Throne Judgment
11 Then I saw a great white throne and Him who sat on it, from whose face the earth and the heaven fled away. And there was found no place for them. 12 And I saw the dead, small and great, standing before God, and books were opened. And another book was opened, which is the Book of Life. And the dead were judged according to their works, by the things which were written in the books. 13 The sea gave up the dead who were in it, and Death and Hades delivered up the dead who were in them. And they were judged, each one according to his works. 14 Then Death and Hades were cast into the lake of fire. This is the second death. 15 And anyone not found written in the Book of Life was cast into the lake of fire.